Tunisia almost took the lead in the opening two minutes, but Ahmed Akaichi's header skimmed the post and he smashed a shot narrowly wide.
In between, Senegal took the lead through Sadio Mane's penalty after Cheikhou Kouyate had been hacked down.
Kara Mbodj powerfully headed in a second, and almost scored an own goal when his clearance struck the post.
Tunisia were guilty of missing plenty of chances, in particular Youssef Msakni, who headed wide from two yards out and shot straight at Abdoulaye Diallo in the second half.
Victory for Aliou Cisse's side means they top their group after Algeria's surprising 2-2 draw against Zimbabwe.
#afcon2017 #TunSen match goals
Watch and download the match highlights and goals in the game between TUNISIA VS Senegal 0-2 at the ongoing #afcon 2017 nations cup below